ODE
\[ -y'''(x)+y''''(x)-3 y''(x)+5 y'(x)-2 y(x)=e^{3 x} \] ODE Classification
[[_high_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0345105 (sec), leaf count = 39
\[\left \{\left \{y(x)\to c_1 e^{-2 x}+e^x \left (x \left (c_4 x+c_3\right )+c_2\right )+\frac {e^{3 x}}{40}\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{3\,x}}}{40}}+{\it \_C1}\,{{\rm e}^{x}}+{\it \_C2}\,{{\rm e}^{-2\,x}}+{\it \_C3}\,x{{\rm e}^{x}}+{\it \_C4}\,{x}^{2}{{\rm e}^{x}} \right \} \] Mathematica raw input
DSolve[-2*y[x] + 5*y'[x] - 3*y''[x] - y'''[x] + y''''[x] == E^(3*x),y[x],x]
Mathematica raw output
{{y[x] -> E^(3*x)/40 + C[1]/E^(2*x) + E^x*(C[2] + x*(C[3] + x*C[4]))}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)-diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)+5*diff(y(x),x)-2*y(x) = exp(3*x), y(x),'implicit')
Maple raw output
y(x) = 1/40*exp(3*x)+_C1*exp(x)+_C2*exp(-2*x)+_C3*x*exp(x)+_C4*x^2*exp(x)